EC is perpendicular to OC. AD is perpendicular to AB.
So EA = EC.
Similarly you can prove that EP = EC.
and EA=EC (equal sides of an isosceles triangle)
(tangents at A and C)
Hence we can conclude that OAEC is a square
(angle in a semicircle)
(angle of a line)
From 1 , we see that
ED=OC (corresponding angle)
Since OC=EA , ED=EA